Stable Sets for Asymmetric Information Economies

An exchange economy with asymmetrically  informed agents is considered with an exogenous rule that regulates  the information sharing among agents. For it, the notion of stable  sets à la Von Neumann and Morgenstern is analyzed. Two different  frameworks are taken into account as regards preferences: a model  without expectations and a model with expected utility. For the first  one, it is shown that the set $V$ of all individually rational, Pareto  optimal, symmetric allocations is the unique stable set of symmetric  allocations. For the second one, an example is presented which shows  that the same set $V$ is not externally stable and a weaker result is  proved. Finally, the coalitional incentive compatibility of  allocations belonging to the unique stable set is provided.